Thursday, June 06, 2013

Lightning strikes me and I die. Fortunately (let's suppose), the universe is infinite and consciousness supervenes on the arrangement of molecules in one's body. So somewhere in my forward light cone -- maybe in about a double-boggle years [note 1], arises an enduring, Earthly, Boltzmann continuant of me.

A Boltzmann continuant for Person X at time T is, I stipulate, any being that, at time T-prime, arises suddenly from disorganized chaos, into a entity particle-for-particle identical to Person X at time T, within an error range of a thousandth of a Planck length. [note 2] A Boltzmann continuant is enduring just in case it survives in human-like form for at least one day. A Boltzmann continuant is Earthly just in case it exists in an environment that, at time T-prime, is particle-for-particle similar to Earth at T, within a range of 10,000 light years, and obeys the same laws of nature -- except allowing for minor differences in features that had not been observed before time T but would be plausible epistemic possibilities to human observers, such as the unobserved top of a cloud twisting one way rather than another, an unobserved flower in the Sierra being one centimeter to the left, differences in the details of how storms play out on distant planets, etc.

According to mainstream physics (back to Ludwig Boltzmann), there is an extremely tiny but finite chance that such an enduring, Earthly, Boltzmann continuant of me could arise. So if the universe exists long enough and doesn't settle into some inescapable loop, presumably I will eventually have a Boltzmann continuant.

By hypothesis, my Boltzmann continuant is not killed by the lightning strike; he survives at least one day. Maybe he survives a near miss with lightning. By hypothesis, my Boltzmann continuant will have the same arrangement of molecules in his body at time T-prime as I do at time T; and since the environment is Earthly, presumably things will proceed fairly normally from time T-prime forward, despite the chaos before time T-prime. By hypothesis, consciousness supervenes on the arrangement of molecules, so presumably my Boltzmann continuant will have conscious experiences very much like the ones I would have had if I had not been struck by the lightning. Maybe my continuant will have an episode of thinking to himself something like "Wow, that lightning struck close! I'd better get inside!" [note 3]

Earth is a pretty safe and stable place. So too, then, is continuant-Earth. My continuant returns "home", greets the continuant versions of his family, comes to the continuant version of his office, works on a post for the continuant version of The Splintered Mind. I have no future. He has no past. But we hook together seamlessly into one "Eric Schwitzgebel" with an undetectable double-boggle-year gap between us. Call the entity or quasi-entity composed of these two parts gappy-Eric.

In a way, it would be odd to think it mattered hugely that there is such a gap between these two half-Eric Schwitzgebels. From the inside, gappy-Eric will feel just like he's a continuous, Earthly Eric Schwitzgebel. From the outside, too, at least through the next 10,000 years, no one on continuant-Earth will have cause to suspect a gap in Eric or in the world. Gappy-Eric's family life, his professional life, the whole planet -- all would seem the same, all would seem to continue unabated. Continuant-existence would seem to be survival enough.

Of course, I needn't be struck by lightning for there to be enduring, Earthly, Boltzmann continuants of me. If we accept the that the universe is infinite, diverse, and subject to Boltzmannian chances, then every time slice of me will have an infinite number of enduring, Earthly, Boltzmann continuants somewhere in the future. So I needn't fear any early, chancy death: Some appropriate Boltzmann continuant of me will launch at precisely the right subjective moment to continue me seamlessly. Gappy-Eric lives! In some cases, going back a few seconds might be necessary to find an appropriate time T from which my death was not inevitable in any Earthly environment, but it seems like quibbling to think those few seconds make a huge ontological difference.

With infinitely many continuants of me, sprouting off from every moment of my life, whose continuant-bodies on continuant-Earth are for practical purposes as good a continuation of me as is my own body on Earth, maybe I shouldn't care about my individual death at all, in any circumstances -- or rather maybe I should care about it only as the loss of one soldier in an infinite army of me.

Yes, this is entirely bonkers.

[revised Nov. 19, 2014]

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[note 1]: The number of particles in the observable universe is estimated at about 10^80. Maybe 10^75-ish of those are within 10,000 light years of us. To have enough particles suddenly conform to the structure described in the next paragraph from a previous state of chaos (rather than in some more normal-seeming way) might require a very long time -- longer, perhaps, than the Poincare recurrence time of the observable universe. If 10^100 is a googol and 10^10^100 is a googolplex, let's call a "boggle" 10^10^... [repeated a googolplex times] ...^100. A "double-boggle", then, could be 10^10^... [repeated a boggle times] ...^100. I'm hoping that's big enough.

[note 2]: I assume that differences of less than a thousandth of a Planck length don't matter to consciousness. If necessary, we can narrow the error range. If we use an ontology of fields, presumably an error measure similiar in spirit could be developed. There will also be an issue about temporal spread -- perhaps more serious if consciousness spreads across a specious present. If necessary, there could be a brief period during which consciousness slips into the Boltzmann continuant before full supervenience takes hold.

[note 3]: The question arises whether the continuant's thoughts would have that meaning, if the meaning of words depends on facts about learning history; but given our stipulations, at least the continuant's conscious experience of that episode of inner speech will be like mine would have been, even if it doesn't tack down its reference in the external world in quite the right way.

37 comments:

This isn't much different from the original Swampman. And, in both cases, there's no continuity at all, none. You don't have a Boltzmann Brain continuer. You don't persist in any way into an accidental duplicate. You could appeal to some weak form of temporal counterpart theory. But temporal counterparts usually require some form of continuity (which is why they're not merely modal counterparts).

@ Eric: I agree that similar personal identity considerations would apply to the Swampman case. In preparing this post, I did a quick search of the philosophical literature on personal identity and Swampman and found surprisingly little, apart from an interesting paper in 2005 by Scott Campbell (and a 2013 objection to some details of it not pertinent to the Boltzmann variant). I welcome pointers to other relevant literature.

Of course, if Swampman is not conscious, or not conscious in the same way we are (e.g., Dretske 1995), the argument doesn't work -- hence my immediate supervenience postulation. This post is conditional on denying vehicle externalism about consciousness. But if we grant vehicle internalism, there's something to be said for Swampman being a good-enough continuer.

Consider this hypothetical: Someone tells you that two years ago, you suffered a swamp accident. Do you now think you are two years old and none of your promises or friendships endured across the gap? Or do you pretty much go on as before, unsettled but not de-identified from the Eric of past years? I suggest the latter is the more appropriate reaction.

What the Boltzmann thing adds that Swampman lacks is a non-trivial probability of such a continuant. It is, I think, a cosmological hypothesis with a non-trivial chance of being true that we live in an infinite universe that doesn't settle into an inescapable loop of the sort that would preclude a Boltzmann continuant of you.

I deny that there is any identity through time. I'm a four dimensionalist, ala Ted Sider or David Lewis. And four dimensionalism is ultimately just temporal counterpart theory. So, sure, if I were Swamp-Eric, I wouldn't really care. But I wouldn't in that case be a continuer of the pre-swamp-accident-Eric. I would be a lucky accident. I would bear similarity relations to the Pre-Swamp-Eric, but no continuities. And perhaps similiarity is sufficient for lots of stuff. I'm fine with that.

The problem is that you talk about continuities where there are no continuities at all (e.g. "My Boltzmann Continuants"). And you repeatedly talk about continuity in the article and in your reply. That's just plain false. There is no continuity whatsoever. The existence of the Boltzmann Brain carries no information about me at all; it does not depend on me at all; had I not existed, it would still exist.

There is literature on this, but it's not much related to swampman per se. Hud Hudson writes about it in his Material Persons book (but he just uses his "intuitions" to close the case). Richard Taylor and van Inwagen & others have written about "immaculate replacements" and accidental replicas and whatnot.

Again, if I turned out to have been a swamp accident for the last two years, all that would prove is that similarity trumps continuity. And that might be just fine with me. But similarity is not continuity, and it does not help to confuse the two.

Thanks for clarifying, Eric! I'm not attached to the word "continuant", though it's convenient and lacks the negative loading of "replacement" and "replica". Maybe it has a positive loading instead. (A "replacement" for me, or a "replica" of me, sounds like something that is assumed to be not me, to my ear. Does a "continuant" sound like something that is assumed to be me? It seems more neutral.)

If you don't care that you are now (let's suppose) Swamp-Eric, that's enough for the core of my argument. I'm thinking that if you don't care that you are now Swamp-Eric, then you shouldn't care about the gap in a Boltzmann-created gappy-Eric -- at least insofar as you are self-centeredly unconcerned about the Earthly people who mourn you. And then, if you knew the universe was infinite and had Boltzmann events, that might have an influence on your view of what's worth worrying about in lightning storms.

My own 4D view is that continuity (by which I really mean continuity) of some information carrying sort is needed for temporal counterparts. So I'd still give you philosophical grief of a rather esoteric kind.

Still, you should be honest, and just say that the Boltzmann You is neither a continuant nor even a replica (it's not a replica - a replica carries information about its original).

The Boltzmann Eric is just an imposter, a surrogate, a representative. The point would be to press this very point: yeah, I'm an imposter. So what. Nobody notices and nobody cares. This would be a nice argument against the apparent (but, on your view, vacuous) requirement of some sort of authenticity.

Of course, there's no identity here at all - Swamp Eric isn't Eric. But as a 4D-ist, I say there's no identity through time at all. No worries there. I am replaced by a surrogate every few pico-seconds or Planck intervals or whatever. Still, I'll say that my replacement depends on me. Identity isn't the issue here at all - there's no identity through time.

Now, if I were really to go down the Buddhist road of no-self, which is attractive, I might really say: yeah, even dependency is irrelevant. My imposter really is entirely, completely, perfectly sufficient.

In the same vein as Campbell, but earlier, is Kolak and Martin's (1987) "Personal Identity and Causality: Becoming Unglued".

They discuss what they call "Random Match Examples", of which one that comes closest to your scenario is that involving a supercomputer (K&M, p.343). They also discuss a quantum-mechanical version of it (p.344), which asks us to entertain the possibility that there is no causal continuity at all even in what we consider ordinary cases of day-to-day, moment-to-moment survival.

They then ask whether we would continue to maintain the intuition that there is day-to-day, moment-to-moment survival under this (admittedly unlikely) supposition. They say we would, and I'm inclined to agree (but of course our intuitions can be mistaken). They take this as supporting the claim that the causal condition is not necessary for the preservation of what matters in survival.

"Consider this hypothetical: Someone tells you that two years ago, you suffered a swamp accident. Do you now think you are two years old and none of your promises or friendships endured across the gap? Or do you pretty much go on as before, unsettled but not de-identified from the Eric of past years? I suggest the latter is the more appropriate reaction."

It seems to me that we tend to be more nonchalant about past misfortunes that befell us, than we are about future misfortunes. If you tell me that I will suffer a swamp accident two years from now, I suspect that there would be no philosophical reasoning to placate my fear.

Boltzmann was not merely pre-quantum, he was pre-relativity. The whole things hinges on that pesky little word "infinite". Much beloved by mathematicians. Physicists, not so much. I Am Not A Physicist, but I am told the Standard Model still calls for a universe that is "finite but unbounded". In about 100 trillion years nearly all matter not locked up in black holes will have been converted into background radiation. A quadrillion years or so after that, the last black hole will evaporate. and there will be a big fat Nothing at a uniform 2-3 degrees above absolute zero. Physics, with its usual disdain for nomenclature, calls this the Heat Death of the Universe (why not Cold Death?). That's still a lot of time, space and matter between here, and now, but perhaps not enough for the Boltzmann scenario. You'd have to go sideways into multiverse theory to get the elbow room. I recall we've been there before. Still, let's explore.

1. going along this chain of reasoning, your Boltzmann continuant would himself have at least one Boltzmann continuant. In fact there is an endless chain of Boltzmann continuants stretching forwards. So, you are already immortal, but getting increasingly decrepit. But fear not! In at least one of the side branches, one of your continuants is bound to stumble upon the secret of eternal youth. Congratulations.

2. Equally, there must be an endless chain of continuants (preceduants?)stretching backwards. Yet we persist in talking as if we were the original, from which the continuants split off. Why the privileged position? Why even assume that there IS an original out there somewhere in time? There could be nothing but the series of Boltzmann brains.

Oops gotta go, faculty meeting. See you again in ... 47.973 million years, OK?

I had a reaction similar to Eric Steinhart's. What you call Boltzmann Continuants are not proper continuations, because their states do not depend on yours. So as not to beg the question as to it's status, let's call the candidate continuant Boltz Man. If (counterfactually) you had lost a finger in a sledding accident as a child, Boltz Man would still have ten fingers. There is assured to be some other candidate continuant with only nine fingers, but it wouldn't be Boltz Man.

As for the question you ask in comments, how I would feel if you told me I was in fact a Swampman of the original P.D. Magnus: I would not (contra Eric) say that the earlier guy was someone else other than me. Rather, I would simply not believe you. There is no possible evidence you could show me which would convince me that I was such a Swampman. This isn't just being contrarian. Rather, it makes me think that my intuitions about Swampman are not at all probative.

A final note: Eric connects his reply to four-dimensionalism, but that really seems like a separate issue. A 4Dist might either affirm or deny that Boltz Man is a future Schwitzgebel, depending on how they construe the temporal counterpart relation.

@ Eric: Thanks for "continuing" to push on this. I think our views substantively aren't too far apart except for our terminological dispute. I like the term "continuant", and I hope that I can define it in the sense of the post without jarring *too* badly against ordinary and technical usage -- though I agree it jars at least somewhat. Your proposed alternatives "imposter", "surrogate", "representative", etc., mostly seem worse to me -- too loaded. I am inspired to keep my eyes open for a good replacement term.

I'm inclined to think "identity" is a red herring, as you seem also to think. I basically accept Parfit's arguments against giving it the kind of importance traditionally assigned.

Boram: Thanks for the reference to Kolak and Martin; I hadn't seen that one. And interesting point about past vs. future. I'm inclined to think (a.) that if I really *knew* it would be a full-on Swampcase, then (assuming internalism) I shouldn't think of it as death in the full-on sense in which death is horrible; and (b.) that the future case is less meritorious as a thought experiment than the past case, because if it's truly random, how would you know that it will be a proper Swampcase? Maybe the way to save it is to transform it into an infinite-universe case like in my original post; but then we're back where we started.

On your first point: "A quadrillion years or so after that, the last black hole will evaporate. and there will be a big fat Nothing at a uniform 2-3 degrees above absolute zero". Right. So the question is: Will the universe be *stuck* there? Then it would be what I referred to as an "inescapable loop". Or, could the universe -- as long as there's infinite time -- eventually pop into a low-entropy states by chance? My sense of the literature is that the latter is at least a respectable opinion. So the scenario is hypothetical upon the latter being the truth.

On your 1 and 2: Right. I didn't want to push too far on those things in this post, but absolutely, if we buy this Boltzmann proliferation, then all kinds of other wacky stuff follows too. I explore some of that in my post on Nietzsche's eternal return scrambled sideways. (I can't recall if you commented on that post or not.)

P.D.: Right, that's all sensible. Interesting to hear that you're with Eric Steinhart on the misleadingness of "continuant". But there really does need to be some general term, and it's nice to choose a term that fits with the final conclusion rather than begging the question against it. "Duplicate" or "replica" isn't too bad, but besides suggesting "not me" the terms also suggest that duplicates/replicas have overlapping stretches of subjective experience (both Eric and d-Eric experience Kate/d-Kate's kindergarten graduation). The nice thing about "continuant" in contrast is that it suggests -- right up front in the title -- that the new being just picks up where the old being left off. "Boltzmann duplicates" suggests something very different on its face than does "Boltzmann continuants" -- something closer to what I explored in my post on Nietzsche's eternal return.

What about "counterpart"? That strikes me as being neutral on the question of whether Boltz Man is a genuine continuation of your life (and so a continuant in a strict sense), a duplicate (and so a copy or replica in a strict sense), or a just an unconnected, coincidentally similar thing. The question is whether this counterpart relation is the one that matters for personal continuity across time.

" Or, could the universe -- as long as there's infinite time -- eventually pop into a low-entropy states by chance?"

Einstein was once asked to explain relativity in layman's terms. He said that before relativity, we thought that if you took away all matter, space and time would still exist. But relativity teaches us that with matter gone, space and time too cease to be meaningful constructs.

I agree with P.D. -- just use the term "counterpart". Nobody will give you grief about that, since a counterpart is indeed what it is. (And you're not going to fool anybody by calling it a continuant, it isn't a continuant at all.)

This is a bit of a hijack, but here goes. (I just thought of it while thinking about your post.) An argument against an infinite universe.

The great Raymond Smullyan offers this "curious puzzle:"

Imagine that you have a solid plane table with a finite rod bolted perpendicular to its surface. One end of an infinite rod is hinged perpendicular to the top of this finite rod (parallel to the surface of the table). The hinge allows the infinite rod to move up and down, but the curious thing is that the rod cannot possibly move down because both it and the table are solid and if it moved down it would intersect the table. And so, you have the curious phenomenon of the hinged rod being supported at only one end.

So the argument against an infinite universe goes like this.(1) Assume the universe is infinite.(2) If the universe is infinite, then Smullyan's scenario is possible.(3) If Smullyan's scenario is possible, then the laws of physics as we know them are incorrect.

I don't have much to say in defense of (2). One way to resist (2) is to point out that an infinite universe does not imply infinite matter. But arguably, your Boltzmann argument requires infinite matter, so you probably wouldn't take that approach. One could argue that the vertical rod would break, or something like this, but this objection strikes me as suspiciously practical.

Regarding (3), I'm not a physicist, but according to what I was taught, an object can remain at rest (and not rotate) only if the net torque on it is zero. The net torque on the long rod is non-zero, so it should not remain at rest.

If we accept both (2) and (3), then we should conclude that an infinite universe is incompatible with the laws of physics as we know them. And I think this counts against an infinite universe. And this is one way to address Boltzmann-style worries.

Eric & PD: Thanks for the suggestion. I'm inclined to think that "counterpart" also implies not-me, both in ordinary language and in most philosophical usage. But maybe it will do, if consensus is that "continuant" is too problematic.

Zach: Interesting objection -- hadn't heard that one. I reply with a dilemma. Either you mean "nomologically possible" or you mean "conceptually possible". If you mean the former, I deny that the set-up is possible. It would be a violation of the laws of physics for anything to be that rigid. If you mean the later, then I deny the impossibility: It violates the laws of physics, but that's irrelevant to conceptual possibility.

Is there some third species of modality for which the argument works -- metaphysical possibility, maybe? I've never really understood metaphysical possibility except to the extent it collapses into one of those other two modalities, but my opinion about that isn't entirely settled.

That's a really nice objection. It settles the issue for me. I concede the point.

Also, I'm glad to see you say that you have some confusions about metaphysical possibility. I have long felt similarly, but I haven't felt comfortable saying so. Of the three (conceptual, nomological, metaphysical), metaphysical possibility seems to be the one that gets the most action from philosophers.

Could you elaborate on your claim that Swamp-X has no "continuity of some information carrying sort"? It seems to me that an atom-for-atom reproduction of X embodies the dispositions, memories, etc - in short, all of the effects of X's genetic and environmental history.

One might quibble about whether there is nevertheless "continuity" in some strict sense, but that strikes me as way down the list of objections to these thought experiments. So, in the case of Swamp-X, "continuant" seems fine.

In the Boltzman case, a better descriptor might be something like "recurrent-X". But I'd claim that recurrent-X could only logically arise in a recurrence of some subset of X's world sufficient to provide the same genetic and environmental history - thereby greatly reducing the probability of recurrence and hence greatly increasing the MTBR.

You should check out the relevant work on temporal counterpart theory. Four-dimensionalists generally deny identity through time, so, of course your counterparts are not identical to you. And this is true for ordinary life as well. I am not identical to any of my past or future selves. We are all distinct 3D objects existing in distinct times.

But times are like worlds, and temporal operators are like modal operators. Thus it is true that I will be identical with my future selves, and I was identical with my past selves. I will be the same person as my future self and I was the same person as my past self. But "was" and "will be" are temporal operators, which take us to past and future times. You can find all this in Sider's "All the World's a Stage", as well as his Four Dimensionalism book; also in articles and books by Hawley etc.

Your Boltzmann Self would just be a future counterpart, and you could truly say that you will be identical to it. (Again, tense matters: I will be P is not equivalent to I am P, just as I might be P is not equivalent to I am P.)

@Charles - Your Boltzmann Self will exist whether or not you exist. It does not have any of its features because you had yours. It is utterly independent of you. A blind man who had never heard of New York City might scribble on a sheet of paper; I might later pick it up and use it quite successfully as my guide to the NYC subway system. It might be exactly isomorphic to a subway map. But it is not a subway map. It carries no information about the subway. It does not represent the NYC subway. It resembles it, but the resemblance is an accident, a lucky coincidence.

sorry for the rather ugly first comment, I tend to overreact against most things that hook up infinity, consciousness and hypothetical physical legitimacy.

to respond more in line, I find the idea of Boltzmann continuants (I remain skeptical of the actual chances) to be no more ethically/morally (not sure what is the proper term here) relevant than the fact there are/were/will be other people thinking, doing, experiencing in a similar way to you. you as a particular sum-total of experience, recorded and processed in a particular body/brain, will none the less have met its end, no matter the similarity with the particular boltzmann "continuant". an experiencing man at best is a particular implementation of a certain form of experience, that allows to identify two (or whatever number we want) particulars as "the same", but he's not the form itself. the form itself is not conscious, and probably might be thought of as an abstract description capturing everything that's relevant about the identity of these particulars.hah, what it all comes down to, is "there's no real continuity", but that has already been stated in the comments repeatedly.

Thanks for the reply. FWIW, I agree with almost all of it. My one quibble is with:

Your Boltzmann Self will exist whether or not you exist.

I get your point, but because scenarios like this are so bizarre, I think precision is important. I'd say instead something like:

The probability of a sequence (in time) of organisms that at some point in the existence of each are essentially atom-for-atom identical is non-zero.

(Which I doubt, but I'm willing to play along.)

That formulation avoids the difficult issue of what constitutes a "self", includes no hint of continuity between organisms in such a sequence, and admits the possibility that the history subsequent to the time of the recurrent state can be different for each organism in the sequence. That is, it supports the idea in Eric's post of an organism's history subsequent to a recurring state diverging from a predecessor organism's history subsequent to that state without suggesting any continuity of the "self" of the predecessor organism to the successor organism.

Some confusion may result from failure to distinguish an organism considered as a physical entity and as a social entity. It seems clear that two physically identical organisms separated in space and/or at least some minimum time interval are not the same physical entity. But as you suggest, if "nobody notices and nobody cares" which physical entity is present, they are in that sense the same social entity, ie, person. I've dealt with very young identical twins, in particular playing "guess which is which". When they were five-ish, my infrequent interaction with them and their limited social development didn't result in enough information for me to distinguish them as persons. But since they were standing side-by-side, there was no question at all that they were different physical entities notwithstanding being biologically extraordinarily similar.

In that sense, the members of a sequence of organisms each of which at some point in time achieves a common physical state in a common social environment might be considered to be the same person at those moments. But even so, what might then be said about the relation between the "self" of each is beyond my grasp of that concept.

Ok, the sheer improbablility of the Boltzmann Brain thing is freaking people out. How about a more culturally familiar scenario? The Star Trek transporter analyzes you down to the last quark, then destroys you and recreates you on the surface of a planet. Whether it actually sends your atoms down there or grabs local atoms to do the job is immaterial. In effect, it is an artificially created Boltzmann Brain (this message brought to you by Boltzmann Transporters, Inc, Why wait a billion years? Beam down today!). The basic questions Eric poses can apply to that as easily. Since we know that people can get stuck in the Transporter buffer (the Federation doesn't encourage this, but there have been episodes where it happened)there could be a delay between scan and beam of a second, or a million years. Whichever, out steps a person wholly convinced that he is James T Kirk. and everybody in the Star Trek Universe accepts that as a fact. But is he Boltzmann Kirk?

Contra Steinhart et al, I vote for Schwitzgebel sticking to his guns on calling the BBs "continuants." However, FWIW, I am prone to Humean/Buddhist nihilisms about causation and selves and have strong leanings towards internalist psychophysicalist supervenience.

If there are infinite Boltzmann continuants of myself which one should I expect to be at any instant from the next? I presume either the one most similar to me or the one most likely to occur.

1) The latter scenario looks awfully like real life because if I am in a car crash then the most likely scenario may be for me to be injured and there may be a continuant from one instant to another - just one that follows a path leading to my death. The paths that have me being like I am now get rapidly shut off from being possible continuations of myself.

2) If it is the former scenario maybe I would expect to have an unusually usual life - i.e. getting the most common outcome a unreasonable amount of the time. come to think of it that may be true for me!

Interesting points, GNZ! I guess I'm assuming that the notion of a *single* best continuant is problematized, and thus that we probably need to let go of identity in the strict logical sense. But if we want to hold onto something like a best-continuer, I agree the issues you raise become problems!